EFFECT OF PARTICLE SIZE IN ANALYSIS OF CREEP IN AN ISOTROPIC UNIFORM COMPOSITE CYLINDER

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INTERNATIONAL JOURNAL OF INNOVATIONS IN ENGINEERING RESEARCH AND TECHNOLOGY [IJIERT]
ISSN: 2394-3696
VOLUME 2, ISSUE 7, JULY-2015
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EFFECT OF PARTICLE SIZE IN ANALYSIS OF CREEP IN AN
ISOTROPIC UNIFORM COMPOSITE CYLINDER
Prof. Vyankatesh S. Kulkarni
Department of Mechanical Engineering,
Solapur University /BIT/Barshi/India
ABSTRACT
The following paper discusses the effect of particle size in analysis of creep in an isotropic
uniform composite cylinder. The paper is a part of the series of papers published under the
analysis of creep in an isotropic uniform composite cylinder.
INTRODUCTION
In applications such as pressure vessel for industrial gases or a media transportation of high-
pressurized fluids and piping of nuclear reactors, the cylinder has to operate under severe
mechanical and thermal loads, causing significant creep hence reduced service life (Gupta and
Phatak, 2001; Tachibana and Iyoku, 2004; Hagihara and Miyazaki, 2008). As an example, in the
high temperature engineering test reactor, the temperature reaches of the order of 900oC
(Tachibana and Iyoku, 2004). The piping of reactor cooling system are subjected to high
temperature and pressure and may be damaged due to high heat generated from the reactor core
(Hagihara and Miyazaki, 2008). A number of studies pertaining to creep behaviour of the
cylinder assume the cylinder to be made of monolithic material. However, under severe thermo
mechanical loads cylinder made of monolithic materials may not perform well. The weight
reduction achieved in engineering components, resulting from the use of aluminum/aluminum
base alloys, is expected to save power and fuel due to a reduction in the payload of dynamic
systems. However, the enhanced creep of aluminum and its alloys may be a big hindrance in
such applications. Aluminum matrix composites offer a unique combination of properties, unlike
many monolithic materials like metals and alloys, which can be tailored by modifying the
content of reinforcement. Experimental studies on creep under uniaxial loading have
demonstrated that steady state creep rate is reduced by several orders of magnitude in aluminum
or its alloys reinforced with ceramic particles/whiskers like silicon carbide as compared to pure
aluminum or its alloys (Nieh, 1984; Nieh et al, 1988). A significant improvement in specific
strength and stiffness may also be attained in composites based on aluminum and aluminum
alloys containing silicon carbide particles or whiskers. In addition, a suitable choice of variables
such as reinforcement geometry, size and content of reinforcement in these composites can be
used to make the cost-effective components with improved performance. With these
forethoughts, it is decided to investigate the steady state creep in a cylinder made of Al-SiCp
composite and subjected to high pressure and high temperature. A mathematical model has been

developed to describe the steady state creep behaviour of the composite cylinder. The developed
model is used to investigate the effect of material parameters viz particle size and particle
content, and operating temperature on the steady state creep respon
Fig. No.1 Schematic of closed end, thick
Fig. No. 2 Free body diagram of an element of the composite cylinder
EFFECT OF PARTICLE SIZE
Figure 3 shows the distribution of radial, tangential, axial and effective stresses in the composite
cylinder for varying size of SiCp reinforcement from 1.7
remains compressive over the entire radius, with maximum and minimum valu
the inner and outer radii, under the imposed boundary conditions
VOLUME 2, ISSUE
eveloped to describe the steady state creep behaviour of the composite cylinder. The developed
content, and operating temperature on the steady state creep response of the composite cylinder.
Schematic of closed end, thick-walled composite cylinder subjected to internal
and external pressures.
Free body diagram of an element of the composite cylinder
EFFECT OF PARTICLE SIZE
shows the distribution of radial, tangential, axial and effective stresses in the composite
cylinder for varying size of SiCp reinforcement from 1.7 µm to 45.9 µm. The radial stress
remains compressive over the entire radius, with maximum and minimum values respectively at
the inner and outer radii, under the imposed boundary conditions given in Eqs. Below
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eveloped to describe the steady state creep behaviour of the composite cylinder. The developed
se of the composite cylinder.
walled composite cylinder subjected to internal
Free body diagram of an element of the composite cylinder
shows the distribution of radial, tangential, axial and effective stresses in the composite
. The radial stress
es respectively at
Below

The tangential stress varies from maximum compressive value at the inner radius to reach a
maximum tensile value at the outer radius of the cylinder.
of radial and tangential, stresses, Eqn. below
Exhibits a variation similar to that observed for tangential stress. The variation in size of
reinforcement (SiCp) does not exhibit a sizable effect on the values of stresses in the cylinder,
except for some marginal variation observed in tangential stress near th
The maximum variation observed for tangential stress is about 4
outer radius whereas for axial stress the variation observed is less than 1
about 2% at the outer radius of th
those observed for cylinder having finer SiCp of size 1.7
compressive (near the inner radius) as well as tensile (near the outer radius), in the cylinder
having finer sized SiCp (1.7 µm
relatively coarser SiCp (i.e. 14.5
from the inner to the outer radius of the cylinder. With the increase in SiC
45.9 µm, the effective stress exhibits a marginal increase near the inner radius but it decreases
marginally towards the outer radius.
The strain rates, given by Eqs below
Are dependent on the effective strain rate
difference of effective stress σe and threshold stress
below
Therefore, to investigate the effect of reinforcement (SiCp) size on the creep rates, the variation
of stress difference (σe-σ0).
Is plotted with radial distance in Fig below
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maximum tensile value at the outer radius of the cylinder. The axial stress, which is the average
s, Eqn. below
a variation similar to that observed for tangential stress. The variation in size of
except for some marginal variation observed in tangential stress near the inner and outer radii.
The maximum variation observed for tangential stress is about 4% at the inner as well as at the
outer radius whereas for axial stress the variation observed is less than 1% at the inner radius and
at the outer radius of the cylinder having coarser SiCp of size 45.9 µm
those observed for cylinder having finer SiCp of size 1.7 µm. The tangential stresses, both
µm) are marginally higher than those observed in cylinders with
14.5 µm and 45.9 µm). The effective stress decreases on moving
from the inner to the outer radius of the cylinder. With the increase in SiCp size from 1.7
, the effective stress exhibits a marginal increase near the inner radius but it decreases
marginally towards the outer radius.
below
dependent on the effective strain rate έe which ultimately depends upon (
and threshold stress σ0 as evident from creep law given by
ith radial distance in Fig below
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The axial stress, which is the average
a variation similar to that observed for tangential stress. The variation in size of
e inner and outer radii.
at the inner as well as at the
at the inner radius and
µm as compared to
. The tangential stresses, both
) are marginally higher than those observed in cylinders with
). The effective stress decreases on moving
p size from 1.7 µm to
, the effective stress exhibits a marginal increase near the inner radius but it decreases
ultimately depends upon (σe-σ0). The
as evident from creep law given by Eqn.

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Fig 3 Variation of creep stresses for varying particle size of SiC (V = 10 vol%, T = 350 °C).
It is noticed that the stress difference (σe-σ0) decreases significantly over the entire radius with
decreasing SiCp size from 45.9 µm to 1.7 µm. The decrease observed may be attributed to the
increase in threshold stress with decrease in particle size as evident from Table below
Table.No.1 Creep parameters for Al-SiCp composites (Pandey et al, 1992)
As consequence, the effective strain rate έe also reduces significantly over the entire radius with
decreasing particle (SiCp) size, Fig. given below

Fig no. 4 Variation of strain rates for varying
The decrease observed is about two orders of magnitude with decrease in SiCp size from 45.9
µm to 1.7µm. It is quite evident from Eqn. given above
strain rate is due to decrease in parameter
size of SiCp, as revealed from Table 3.1. The radial and tangential
magnitude but have opposite nature due to the incompressibility condition, Eqn.
and the assumption of plane strain condition
(tensile) strain rates in the cylinder for a given size of SiCp reinforcement are 13
the corresponding effective strain rates, Eqn.
As is also evident from Fig no. 4
observed for effective strain rate. Therefore, it may be concluded that the steady state creep rates
in the composite cylinder could be significantly reduced by
reinforcement in aluminum matrix. For the same volume fraction of reinforcement, the smaller
size particles will be larger in number, and therefore lead to more load transfer to the
reinforcement with a corresponding reduction
material, which enhances the substructure strength (Li and Langdon, 1993; Peng
1999; Han and Langdon, 2002) and ultimately helps in restraining the creep flow of composite
cylinder.
SELECTION OF MATERIAL PARAMETERS
It is evident from the above discussion that the creep stresses in a thick composite cylinder do
not vary significantly by varying size and content of reinforcement (SiCp) as compared to the
variation observed in strain rates.
vessel, operating under elevated temperature, the strain rates are considered to be primary design
parameters. In order to reduce the steady state creep rates in the composite
under a given set of operating conditions (
following three options could be employed: (i) using finer size of reinforcement (SiCp) without
VOLUME 2, ISSUE
Variation of strain rates for varying particle size of SiCp (V = 10vol%
. It is quite evident from Eqn. given above that the decrease observed in effective
to decrease in parameter M and increase in threshold stress σ0
size of SiCp, as revealed from Table 3.1. The radial and tangential strain rates are equal in
magnitude but have opposite nature due to the incompressibility condition, Eqn.
and the assumption of plane strain condition έZ=0 The radial (compressive) and tangential
the cylinder for a given size of SiCp reinforcement are 13
the corresponding effective strain rates, Eqn. below
Fig no. 4 the effect of particle size on strain rates is similar to that
in the composite cylinder could be significantly reduced by employing finer size of SiCp
reinforcement with a corresponding reduction in the level of effective stress shared by the matrix
material, which enhances the substructure strength (Li and Langdon, 1993; Peng
TION OF MATERIAL PARAMETERS
variation observed in strain rates. From The point of view of designing composite pressure
parameters. In order to reduce the steady state creep rates in the composite Cylinder, working
given set of operating conditions (i.e. operating pressure and temperature) any of the
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vol%, T = 350 °C).
that the decrease observed in effective
0 with decreasing
strain rates are equal in
magnitude but have opposite nature due to the incompressibility condition, Eqn. we obtained,
=0 The radial (compressive) and tangential
the cylinder for a given size of SiCp reinforcement are 13% lower than
effect of particle size on strain rates is similar to that
employing finer size of SiCp
in the level of effective stress shared by the matrix
material, which enhances the substructure strength (Li and Langdon, 1993; Peng et al, 1998;
The point of view of designing composite pressure
Cylinder, working
operating pressure and temperature) any of the

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varying its content, (ii) incorporating higher amount of dispersoids (SiCp) without altering its
size, and (iii) simultaneously decreasing the size and increasing the amount of SiCp
reinforcement. The selection of optimum size and content of the reinforcement in a composite
pressure vessel, working under a given set of operating conditions, can be decided by
simultaneously optimizing the cost of composite and the value of maximum strain rate in the
composite cylinder for different combinations of particle size and particle content within the
specified range.
Fig No. 5 Variation of stress difference for varying particle size of SiC (V = 10 vol%, T = 350 °C).
RESULTS AND DISCUSSION
Numerical calculations have been carried out to obtain the steady state creep response of the
composite cylinder for different particle size, particle content and operating temperature.
VALIDATION
Before discussing the results obtained, it is necessary to check the accuracy of analysis carried
out and the computer program developed. To accomplish this task, the tangential, radial and
axial stresses have been computed from the current analysis for a copper cylinder, the results for
which are available in literature (Johnson et al, 1961). The dimensions of the cylinder, operating
pressure and temperature, and the values of creep parameters used for the purpose of validation
are summarized in Table 3.2.
Table no.2 Summary of data used for validation (Johnson et al)

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To estimate the values of parameters M and o for copper cylinder, firstly σ e have been calculated
at the inner and outer radii of the cylinder by substituting the values of σe σr σθ σz in Eqn. we
obtained at these locations, as reported in The study of Johnson et al (1961). The values of
stresses σr σθ and σz and the tangential strain rate έθ reported by Johnson et al (1961) at the inner
and outer radii are substituted in Eqn. we know to estimate the effective strain rates at the
corresponding radial locations. The effective stresses and effective strain rates thus estimated at
the inner radius σe = 189.83MPa and έe = 2.168x10-8
s-1
and at the outer radius σe = 116 MPa έe =
1.128x10-9
s-1
of the copper cylinder are substituted in creep law, Eqn. obtained above, to obtain
the creep parameters M and o for copper cylinder as given in Table 2. These creep parameters
have been used in the developed software to compute the distribution of tangential strain rate in
the copper cylinder. The tangential strain rates, thus obtained, have been compared with those
reported by Johnson et al (1961). A nice agreement is observed in Figures above verifies the
accuracy of analysis presented and software developed in the current study.
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EFFECT OF PARTICLE SIZE IN ANALYSIS OF CREEP IN AN ISOTROPIC UNIFORM COMPOSITE CYLINDER

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EFFECT OF PARTICLE SIZE IN ANALYSIS OF CREEP IN AN ISOTROPIC UNIFORM COMPOSITE CYLINDER